1. Simplify the equation:
The given equation is:
2x + 3 + 1 = 7x + 15 + 3
Combine like terms on both sides:
2x + 4 = 7x + 18
2. Isolate the variable:
Subtract 2x from both sides:
4 = 5x + 18
Subtract 18 from both sides:
-14 = 5x
3. Solve for x:
Divide both sides by 5:
x = -14/5
4. Check the solution:
Substitute x = -14/5 into the original equation:
2(-14/5) + 3 + 1 = 7(-14/5) + 15 + 3
-28/5 + 4 = -98/5 + 18
(-28 + 20)/5 = (-98 + 90)/5
-8/5 = -8/5
The left-hand side equals the right-hand side, so the solution is correct.
Therefore, the solution to the equation 2x + 3 + 1 = 7x + 15 + 3 is x = -14/5 or x = -2.8